The present invention relates generally to missile guidance.
The traditional approach to missile guidance is to use Proportional Navigation (PRONAV). PRONAV was developed by C. Yuan at RCA Laboratories during World War II using physical intuition [1]. The resulting simplistic guidance law states that the commanded linear acceleration .alpha..sub.c is proportional to the line-of-sight (LOS) rate .sigma..sub.T. The proportionality constant can be broken down into the product of the effective navigation ratio N times the relative missile-target closing velocity Vc, EQU a.sub.c =NV.sub.c .sigma..sub.T (1)
Two decades later, the quasi-optimality of PRONAV was derived [2]. The prefix quasi is used here because of all the assumptions that must be made in deriving PRONAV as a solution of a linear-quadratic optimal control problem [3]. These assumptions are as follows:
1. The target has zero acceleration. PA1 2. The missile has perfect response and complete control of its acceleration vector. PA1 3. The missile is launched on a near collision course such that the line-of-sight (LOS) angles remain small over the entire engagement. PA1 4. The missile has zero acceleration along the LOS over all time. PA1 5,168,277--LaPinta et al PA1 5,062,056--et al PA1 5,035,375--Friedenthal et al PA1 4,993,662--Barnes et al PA1 4,980,690--Fiden PA1 4,959,800--Woolley PA1 4,825,055--Pollock PA1 4,719,584--Rue et al PA1 4,568,823--Dielh et al PA1 4,402,250--Baasch PA1 4,162,775--Voles
Since all these assumptions are violated in a typical air-to-air intercept scenario, PRONAV is not realistically an optimal guidance law. In an attempt to account for target acceleration (avoid using the first assumption), an additional term is added to the basic PRONAV equation. The additional term is simply the target's estimated acceleration a.sub.T multiplied by a proportionality coefficient K. This coefficient is a function of time-to-go, which is defined as the time remaining to missile impact or detonation. The resulting guidance law, known as Augmented PRONAV is given in its general form as EQU a.sub.c =NV.sub.c .sigma..sub.T +Ka.sub.T (2)
There are two main reasons that so many assumptions have to be made in relating PRONAV to a linear-quadratic optimal control formulations. First, PRONAV mixes a translational quantity, commanded linear acceleration .alpha..sub.c with an angular quantity, line-of-sight rate .sigma..sub.T. This results in nonlinear dynamics in the associated optimal control problem. Second, PRONAV attempts to directly minimize miss distance, which requires having to estimate time-to-go. A consistently accurate estimate of time-to-go cannot be obtained in a maneuvering target scenario, since the target's future motion is unknown.
These negative characteristics of PRONAV motivated the development of the guidance laws presented herein.
The following United States patents are of interest.
None of the cited patents disclose Proportional Guidance and/or Proportional Guidance and Augmented Proportional Guidance which are based on two guidance law algorithms. The patent to Pollock discloses the use of a trajectory correction algorithm for object tracking. The remaining patents describe a variety of different tracking methods which are of less interest.
The following prior publications are of interest.
Yuan, C. L., "Homing and Navigation Courses of Automatic Target-Seeking Devices," RCA Labs, Princeton, N.J., Report PTR-12C, December 1942. PA0 Yuan, C. L., "Homing and Navigation Courses of Automatic Target-Seeking Devices," Journal of Applied Physics, Vol. 19, December 1948, pp. 1122-1128. PA0 Fossier, M. W., "The Development of Radar Homing Missiles," Journal of Guidance, Control, and Dynamics, Vol. 7, November-December 1984, pp. 641-651, PA0 Riggs, T. L. and Vergez, P. L., "Advanced Air-to-Air Missile Guidance Using Optimal Control and Estimation," USAF Armament Laboratory, AFATL-TR-81-52, June 1981. PA0 Zarchan, P., Tactical and Strategic Missile Guidance, Volume 124, Progress in Astronautics and Aeronautics, Published by the American Institute of Aeronautics and Astronautics, Inc., Washington D.C.